Il Nuovo Cimento B (1971-1996)

, Volume 102, Issue 6, pp 593–608 | Cite as

Convected time derivatives in continuum mechanics

  • P. G. Appleby
  • N. Kadianakis
Article
First Online:
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Summary

In this work we develop a frame-independent approach to the notion of convected derivation, and give a systematic classification of these derivatives in terms of an absolute vorticity and deformation rate in classical space-time. In the case of derivatives following a motion we distinguish between intrinsic and extrinsic convected derivatives. A link is established between the class of convected derivatives and the class of affine connections on classical space-time compatible with its metric structure.

PACS

03.40 Classical mechanics of continuous media: general mathematical aspects 

PACS

02.20 Group theory 

PACS

02.40 Geometry differential geometry and topology 

Конвкутивные временные производные в механике сплошной среды

резюме

В этой работе мы развиваем не зависящий от системы отсчета подход к определению конвективной производной и проводим систематическую классификацию этих производных в терминах абсолютной завихренности и интенсивности деформации в классическом пространстве-времени. В случае производных, определяющих движение, мы различаем собственные и несобственные конвективные производные. Устанавливается связь между классом конвективных производных и классом аффинных связей на классическом пространстве-времени, совместимом с метрической структурой.

Riassunto

In questo lavoro si sviluppa un approccio indipendente dalla struttura alla nozione di derivazione di convezione e di dà una classificazione sistematica di queste derivate nei termini di un assoluto rapporto di deformazione e vorticità nello spazio-tempo classico. Nel caso di derivate che seguono un moto si distingue tra derivate di convezione intrinseche ed estrinseche. Si determina un legame tra la classe di connessioni di convezione e la classe di connessioni affini sullo spazio-tempo classico compatibile con la sua struttura metrica.

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Copyright information

© Società Italiana di Fisica 1988

Authors and Affiliations

  • P. G. Appleby
    • 1
  • N. Kadianakis
    • 2
  1. 1.Department of Applied Mathematics & Theoretical PhysicsUniversity of LiverpoolLiverpoolU.K.
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

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